Toán Lớp 9: cho tam giác ABC có AB=c,AC=b,BC=a .
CMR: a/(b+c-a)+b/(a+c-b)+c/(a+b-c) ≥3
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Toán Lớp 9: cho tam giác ABC có AB=c,AC=b,BC=a .
CMR: a/(b+c-a)+b/(a+c-b)+c/(a+b-c) ≥3
Comments ( 2 )
\dfrac{a}{{b + c – a}} + \dfrac{b}{{a + c – b}} + \dfrac{c}{{a + b – c}} = \dfrac{{y + z}}{{2x}} + \dfrac{{x + z}}{{2y}} + \dfrac{{x + y}}{{2z}}\\
= \dfrac{1}{2}\left( {\dfrac{x}{y} + \dfrac{y}{x} + \dfrac{y}{z} + \dfrac{z}{y} + \dfrac{z}{x} + \dfrac{x}{z}} \right) \ge \dfrac{1}{2}\left( {2 + 2 + 2} \right) = 3\\
\Rightarrow \dfrac{a}{{b + c – a}} + \dfrac{b}{{a + c – b}} + \dfrac{c}{{a + b – c}} \ge 3\\
‘ = ‘ \Leftrightarrow x = y = z \Leftrightarrow a = b = c
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